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Chapter4LandmarkSummaries:InterpretingTypicalValuesandPercentiles,PracticalBusinessStatistics,ChapterTopics,MeasuresofCentralTendencyMean,Median,ModeMidrange,QuartilesExploratoryDataAnalysisFive-NumberSummaryBoxPlot,SummaryMeasures,CentralTendency,Mean,Median,Mode,Midrange,InterquartileRange,Midhinge,SummaryMeasures,Variation,Variance,StandardDeviation,CoefficientofVariation,Range,MeasuresofCentralTendency,CentralTendency,Mean,Median,Mode,Midrange,Midhinge,SampleMean,PopulationMean,TheArithmeticAverageofdatavalues:,TheMean(ArithmeticAverage),SampleMean,PopulationMean,SampleSize,PopulationSize,TheMostCommonMeasureofCentralTendencyAffectedbyExtremeValues(Outliers),TheMean(continued),012345678910,0123456789101214,Mean=5,Mean=6,TheMedian,ImportantMeasureofCentralTendencyInanorderedarray,themedianisthe“middle”number.Ifnisodd,themedianisthemiddlenumber.Ifniseven,themedianistheaverageofthe2middlenumbers.,TheMedian(continued),012345678910,0123456789101214,Median=5,Median=5,NotAffectedbyExtremeValuesForskeweddata,representsthe“typicalcase”betterthantheaveragedoes,TheMode,AMeasureofCentralTendencyValuethatOccursMostOftenNotAffectedbyExtremeValues,Mode=8,012345678910111213,TheMode(continued),ThereMayNotbeaModeThereMaybeSeveralModesUsedforEitherNumericalorCategoricalData,0123456,NoMode,0123456,TwoModes,Midrange,AMeasureofCentralTendencyAverageofSmallestandLargestObservation:,Midrange,Midrange(continued),AffectedbyExtremeValue,012345678910,012345678910,Midrange=5,Midrange=3,Whichsummarytouse?,AverageBestfornormaldataPreservestotalsMedianGoodforskeweddataordatawithoutliers,providedyoudonotneedtopreserveorestimatetotalamountsModeBestforcategories(nominaldata).Themodeistheonlysummarycomputablefornominaldata!,Quartiles,NotameasureofcentraltendencySplitordereddatainto4quarters,25%,25%,25%,25%,Q1,Q2,Q3,SelectedlandmarkstorepresententiredatasetMedian=50thpercentileQuartilesLQ=LowerQuartile=25thpercentileRank=UQ=UpperQuartile=75thpercentileRankisn+1rankoflowerquartileExtremesSmallest=0thpercentileLargest=100thpercentile,Five-NumberSummary,Five-NumberSummary(continued),ProvidesinformationaboutCentralsummaryRangeofthedata“Middlehalf”ofthedataSkewness,ExploratoryDataAnalysis,BoxPlotGraphicaldisplayofdatausing5-numbersummary,Median(Q2),4,6,8,10,12,Q,3,Q,1,X,largest,X,smallest,Spendingrankorderedfromsmallesttolargest0.3,0.6,0.9,1.1,1.4,2.8,3.8,5.512345678LQis(0.6+0.9)/2=0.75UQis(2.8+3.8)/2=3.3,Example:Spending,Example:Spending(continued),Five-numbersummary0.3,0.75,1.25,3.3,5.5BoxplotShowssomeskewness(lackofsymmetry),Exercise,Asystemsmanagerinchargeofacompanysnetworkkeepstrackofthenumberofserverfailuresthatoccurinaday.Thefollowingdatarepresentthenumberofserverfailuresinadayforthepasttwoweeks.30326274023363Obtainthemodeforthesedata,Solution,Theorderedarrayforthesedatais:001223333346726Themosttypicalvalue,ormode,is3.Thus,thesystemsmanagercansaythatthemostcommonoccurrenceistohavethreeserverfailuresinaday.Notethatforthisdatasetthemedianisequalto3andthearithmeticmeanisequalto4.5.Thevalue26isanoutlier;thusthemedianandthemodeisabetterdescriptionofcentraltendencythanthemean.,Exercise,决策者一旦信奉某种无效的行动方针，常会使自己所犯错误逐步升级。组织行为学家和社会心理学家们对这一逐步升级过程产生强烈兴趣。诸如“沉没成本”效应，“陷进泥沼”效应，以及“投入过多，难以自拔”效应，均属这种现象。不过大多数人则把此种现象看作是“落入陷阱”。今有52名初学心理学的大学生参加一项实验室实验，旨在探究将先出现的结果视作自我同一性（主观与客观的一致性）体现的个人倾向，是否会加强上述落入陷阱效应（AdministrativeScienceQuarterly,May.1986）。整个实验由30项试验组成，试验中根据学生判断不同形状几何图形的准确性打分，每项试验的总得分见表。计算这个数据集的平均值、中位数和众数（类）这几个集中趋势量度是否出现在数据分布的中心？,Exercise,54724612111511102342054566155151013946,Solution,mean=9.7Median=7Mode=5b.Theanswerisyes,
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